I believe CTE is real, but not common except in people who have had multiple TBIs. It is a novel diagnosis associated with celebrity athletes and therefore an attractive diagnosis for the media and lay people who get fascinated with unusual or bizarre behaviors that they rarely see but psychiatrists see regularly. I'm a little exasperated by it. It's not entertainment. I had a Bipolar patient behave just like Antonio Brown yesterday, but it was slightly less public and not unusual in patients with poor insight. This patient has erected literal billboards but has not made the national news, thankfully.
I treat many combat veterans who have had multiple TBIs, some may also have CTE, if there is a real difference other than cumulative. They usually have comorbid PTSD, Bipolar, substance use disorders, and other more common psychiatric diagnoses, many times predating the TBI. Certainly there is symptomatic overlap with TBI and other diagnoses. I suspect less athletes have PTSD, but other diagnoses likely have similar prevalence.
To answer your original question: At the end of the day, we treat sympomatically. No, treatment is not dissimilar. The VA has done a lot of research and has many resources about treating TBI, you can Google them and search pubmed as well. Research is ongoing but so far not revolutionary in my view from a practical clinical standpoint. Resources and funding are the main limiting factors in caring for irreversible brain damage, as usual. We see this with other forms of dementia daily.